Quantum behaviors are modeled by two parties making measurements on a shared bipartite quantum state, and in the classical setup, the two parties can share “hidden variables", or shared randomness.
There has been extensive work, for instance, on simulating quantum behaviors with various resources, such as
communication, post-selection, noise and more. There are also strong connections between finding separations between quantum and classical communication complexity, and between quantum and classical zero-communication games.
A survey on quantum non-locality can be found in references [1]}, [2]}, and on the interactions between communication complexity and nonlocality in reference [3]}.
